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Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions

We report on Hybrid-Monte-Carlo simulations of the tight-binding model with long-range Coulomb interactions for the electronic properties of graphene. We investigate the spontaneous breaking of sublattice symmetry corresponding to a transition from the semimetal to an antiferromagnetic insulating phase. Our short-range interactions thereby include the partial screening due to electrons in higher energy states from ab initio calculations based on the constrained random phase approximation [T.O.Wehling {\it et al.}, Phys.Rev.Lett.{\bf 106}, 236805 (2011)]. In contrast to a similar previous Monte-Carlo study [M.V.Ulybyshev {\it et al.}, Phys.Rev.Lett.{\bf 111}, 056801 (2013)] we also include a phenomenological model which describes the transition to the unscreened bare Coulomb interactions of graphene at half filling in the long-wavelength limit. Our results show, however, that the critical coupling for the antiferromagnetic Mott transition is largely insensitive to the strength of these long-range Coulomb tails. They hence confirm the prediction that suspended graphene remains in the semimetal phase when a realistic static screening of the Coulomb interactions is included.